Testing is right. That is actually his true form. The ROTS novelization describes it as the “face of Darth Sidious” or something. He decides at that moment that it could be advantageous to keep it that way since it would appear that he was injured by the Jedi.
ROTS novelization isn’t canon though lol. But like you said, I think it’s more likely that he’s just physically revealing his true form finally (especially with the bonus of looking like Windu messed him up) since we see him use lightning or plunge into the dark side in The Clone Wars multiple times and it never deforms him or Dooku.